MathDB

Rank preservation after interchanging positives and negatives in a matrix

Source: MIPT Undergraduate Competition 2019 1.3

August 17, 2020

linear algebramatrix

Problem Statement

Given a natural number

n

, for what maximal value

k

it is possible to construct a matrix of size

k \times n

consisting only of elements

\pm 1

in such a way that for any interchange of a

+1

with a

-1

or vice versa, its rank is equal to

k